Challenge: To design an accelerating sled system that can drop a cargo a precise distance from a starting position. To be able to model the system mathematically so that you can predict the effect of changes to any parameters.
Parameters: The system must consist of a uniform surface, flat-topped sled of no more than 15 cm in any dimension, and no less than one cm in height, with a cargo of one large metal washer. The sled will be tied to an adjustable mass over a pulley system. You can use the table as a track or add a uniform surface track as part of your set-up. You will need to design and calibrate your system so that you can have the cargo fall off the back of the cart at a predictable position. (The position of impact with the track, not the final resting position). The track can be any length from 60 cm up to the length of the table. The washer should be able to fall off anywhere from 25% to 75% of the length of the track. To achieve particular drop positions, you may not alter the track, pulley, or string in any way, but you can adjust the hanging mass, and/or the initial positioning of the washer on your sled. Your system cannot cause any damage to the table or class materials. Plan on storing your system in your locker between classes, except for perhaps a track if you include one.
Scoring: Your system will be tested in two ways. The first part of the competition will be you demonstrating that your system can hit a desired drop position. You will get the average of three trials. The second part will be your ability to use your mathematical model to predict the changes you will need to make to hit that same position after Mr. J makes an adjustment to one of the controlled parameters of your system. You will need to do that entirely with your model, NOT by trial and error. You will only get to do the run once, after showing Mr. J the results of your mathematical modelling.
Score = relative error in part one + (relative error in part two)0.5. (Low score wins)
Physics: The system will accelerate according to Newton’s Laws. The kinematics can be quantified (eg. Video analysis of the motion with Google Sheets graphs of velocity vs. Time). Friction will be an important factor in your design, and determines when the cargo falls off, but it is difficult to measure directly. The mass of the sled, washer, and the mass hanging on the end of the string contribute to the mass of the system. Free-body diagrams are very helpful, and expected to be part of your model.
Extensions: The pulley has friction and, more importantly, rotational inertia.
The physics of friction is very, very complicated.
Help/Hints: If you want, Mr. J will help you design a pulley system that can pull the sled 150 cm even though your mass can only fall half that distance.
Graph your data from your calibration attempts to see which factors give you the best “tuning ability”. (Changing the falling mass, or changing the initial position of the washer on the sled, or both?). Make sure you can predict the effect of changes to any of the controlled variables on your system so you can do well on part two.